Problem: $z=3-6i$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=-6$ and $\text{Im}(z)=3$ (Choice B) B $\text{Re}(z)=3$ and $\text{Im}(z)=-6i$ (Choice C) C $\text{Re}(z)=3$ and $\text{Im}(z)=-6$ (Choice D) D $\text{Re}(z)=-6i$ and $\text{Im}(z)=3$
Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={3}-{6}i$ is of the form ${a}+{b}i$, where ${a}={3}$ and ${b}={-6}$. Therefore: $\text{Re}(z)={a}={3}$. $\text{Im}(z)={b}={-6}$. Summary $\text{Re}(z)={3}$ and $\text{Im}(z)={-6}$.